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Q & A: atomic energy levels

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Most recent answer: 06/13/2011
Q:
quantum mechanics - energy of sub-shells --------------------------------------- We know that each of the shells has a particular energy value. We further know that the "filling order" of electrons ioto atoms also follows a particlur route. Namely, 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10... We notice that in that "filling order" that the 4s2 gets filled before the 3d10. This would imply, I believe, that he energy of the 4s2 level is "lower" that the 3d10. All of the equations for calculating energy levels that I see are based on determining energies of the "main" shells rather than the sub-shells. So the question is, since I can calculate that the energy level of n=4 is more that the energy level of n=3, how can I justify from an energy standpoint that the higher energy level 4s2 gets filled before the lower energy level 3d10...? thks, Ken
- Ken Baratko (age 65)
Houston,Tx,77092
A:
Very nice question. The nominal energies of those states are based on precise calculations of what the energy would be for a single electron in, say, a 3d state. Once you have other electrons in other states, the energies change a lot. Even the form of the states changes. The 30th electron doesn't see anything like the same distribution of charges that it would have seen if it was the first electron.

So even the order of the energies of the states is affected, mostly because the distribution of distances from the nucleus differs and thus the extent to which they're affected by the other electrons differs.

Mike W.

(published on 06/13/2011)

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